How did mid-19th century American legislation affect the corporate structure of railroad companies?

Question:
How did mid-19th century American legislation affect the corporate structure of railroad companies?

It is my understanding that a part of the complexity that the Standard Oil Company built up was due to the nature of US corporate legislation (while, of course, the rest was that they wanted to hide ownership in other companies, etc) in the 19th century which prevented corporations that were incorporated in one state from engaging in certain activities in another state.

Short Answer:
Yes the rise of Standard Oil was dependent upon the nature of corporate laws in the 1870's specifically the absence of those laws. The business atmosphere given the dearth of regulation/laws created a wild wild west type atmosphere where almost anything could occur. This both motivated and inspired Cornelius Vanderbilt, the wealthiest man in the USA and owner of the most miles of railroad track. It drove Vanderbilt to to seek innovative opportunities, which ultimately what standard oil was in 1975. Vanderbilt's agreement reeked of favoritism and anti competitive rigging of the market and would never have been permitted today or under a properly regulated market.

Detailed Answer
The rise of Standard Oil was entirely dependent upon the nature of US railroads. It wasn't the restrictive nature of corporate laws regarding railroads which Rockefeller took advantage of but rather the lack of them. From 1825-1865 US railroad industry built a huge transportation network. After the Civil War the business changed as the US railroad industry had overbuilt and their was a glut of capacity and lines in the country. This turned the once boom industry into one of cut throat competition.

A mature economy, one of regulations and laws would have handled this better, but that description could not be applied the US in the post war period. The Wealthiest railroad baron at the time was Cornelius Vanderbilt owned more miles of rail than any person in the world, and wealthiest man in the country. One of the wealthiest men in the world. Vanderbilt's plan to weather the market downturn was to use his capital and purchase the very best performing railroads for himself. He targeted the Erie Line which connected New York and Chicago, the most valuable and profitable line in the country at the time. Only because there weren't very good laws governing Corporations at the time the owners of the Erie Line, recognizing what they were up against, chose to sell their stock to vanderbilt while printing new issues of stock simultaneously. (water down the stock). Vanderbilt didn't realize that for every share he purchased, the company was printing two new shares. This is a highly illegal practice today but at the time nobody had every imagined such a thing, so there were no laws against it. The law was actually against Vanderbilt, because the perpetrators enlisted Boss Tweed of NY as an ally / board member of the Railroad, who passed legislation legalizing the new stock shares. Vanderbilt spent nearly 10 million dollars on stock ( 1 billion in todays dollars ) and still didn't control the line. Still worse the owners of the Erie line took delight in giving interviews with newspapers detailing how they had got the better of Vanderbilt. See Erie War

Vanderbilt's now under financial stress and embarrassed by his public defeat over the Erie line, Comes up with a plan B and this is where Standard oil comes into the picture. Vanderbilt decides if he can't control the lines, he'll control the largest customers for rail transportation, the Oil Industry. Oil from the ground was used to make kerosine which fueled the lights for the nation. Kerosine was a cheap, effective light source which was transforming post war country. Prior to the use of Kerosine most Americans didn't have an affordable light source for use after dark. Kerosine forever changed that, and Vanderbilt decided to use this phenomenon to maintain himself at the top of the rail industry.

The United States was at the forefront of this oil innovation and the center of oil refineries and production in the US was Cleveland Ohio. So Vanderbilt began to buy up railroad lines in and around Cleveland, before anybody realized the opportunity. It just so happens that a struggling young 27 year old John D. Rockefeller's refinery was proximal to a railroad line which Vanderbilt purchased. This made Rockefeller's refinery a prime target for Vanderbilt, which got him an audience to meet with Vanderbilt in New York.

Rockefeller a struggling nearly bankrupt very young oil man basically upsells Vanderbilt. Vanderbilt still smarting from his debacle over the Erie line clearly underestimated the young Rockefeller. Instead of selling his refinery to Vanderbilt, Rockefeller signs a deal to fill all of Vanderbilt's trains with his oil, but at a cutrate price of 2/3rd the transportation price. Again this deal as the Erie Line's strategy of watering down the stocks, would be highly illegal today. Rockefeller who's small refinery had no ability of producing such a huge volume of kerosine, used the favorable transportation deal to line up financing and buy up his competitors in Cleveland. Rockefeller who now could transport his Kerosine at a favorable price verse his competitors had eclipsed his competitors ability to compete with him. This deal transformed Rockefeller's small struggling refinery into the major player in the largest oil market in the country. Not because of Corporate law, but really because their were few and unsophisticated laws governing the behaviors of corporations in the 1870s.

The deal worked for both participants. It just worked a little bit better for Young Rockefeller.

Cornelius Vanderbilt
According to The Wealthy 100 by Michael Klepper and Robert Gunther, Vanderbilt would be worth $143 billion in 2007 United States dollars if his total wealth as a share of the nation's gross domestic product (GDP) in 1877 (the year of his death) were taken and applied in that same proportion in 2007. This would make him the second-wealthiest person in United States history, after Standard Oil co-founder John Davison Rockefeller (1839–1937)

Caveat
This is a very difficult broad question to answer because:

1. Railroad Industry changed dramatically from prior to the american civil war and post war. So mid 19th century isn't precise enough date to nail down a meaningful answer. Standard oil was incorporated in 1870 so I'm going to go with the latter half of the 19th century in my answer.
2. If you are asking about tax laws that's a very involved specialty and would be no less involved when dealing with cross state corporations in the 19th century. I would also add that if there was one uniform property of corporate law (especially rail roads) during this time it's the lack of regulation. Railroads were highly profitable and highly corrupt. America's corporate laws were new and untested. Americas anti-trust and monopoly laws were non existent. America's first significant anti trust law. the Sherman anti trust act would not come into effect until 1890, and even then would not be enforced until Teddy Roosevelt comes to office in 1901. It was not uncommon for political machines like the Boss Tweed of Tammany Hall (famous corrupt political machine which ran Ny York for a time) to form partnerships with railroads. Tweed sat on the board of several railroads including the famous Erie line discussed below, before dying in prison for embezzlement.