In Buddhism, is the effect ontologically independent of the cause?

Cause and effect are not independent but are meditated by mind.

Good householder,

As for Unbound, Nibbana, yes, it's independent from cause, all else, no, no single phenomena can be found in the world, not depending on cause.

Suññata, how ever, is conditioned, required nourishment.

[Not given for stacks, exchange, world-binding trades of other kind but to be used torward the Unconditioned]

In Buddhism, is the effect ontologically independent of the cause?

It depends which Buddhism, and especially which insight tradition. But for the Madhyamaka the answer is a definitive no.

Why? Because effects depend upon causes and causes depend upon effects.
Moreover, all compounded phenomena - that is all existent 'things' arise in dependence upon causes and conditions. Nothing is independent. In Madhyamaka Buddhism, the interdependent arising, momentary change, and eventual dissolution of all existent things demonstrates their lack of objective, independent, intrinsic, inherent, or essential existence. It is because of the fact of causality that there is no ontological independence. Indeed, ontological independence is what is known as 'self' - and the refutation of this - the emptiness or lacking of self in all phenomena, is emptiness, which answers your second question:

what has that got to do with 'emptiness', in any Mahayana tradition?

TL:DR; 'ontological independence' is a fiction - a fiction that ignorance superimposes upon all phenomena, especially our personal aggregates. Being a fiction it is naturally absent from all phenomena (all fictions are naturally absent). The natural absence of this fiction is called 'suchness'. The general term for the absence of inherent existence (aka ontological independence) is emptiness - which is merely shorthand for 'empty of inherent existence', where 'empty' merely means 'lacking'.

Why is the natural absence of a fiction important in Buddhism? Because we naturally assume it to be present - and this assumption is toxic, destructive, and binds us to continuing torment.

It is good to supply sources. Here is Candrakirti commenting on Aryadeva's 400 verses:

"We are not proponents of nonexistence, for we are proponents of dependent-arising." Are we proponents of real (ontologically independent) things? No because we are proponents only of dependent-arising. What is the meaning of dependent-arising? It means the absence of intrinsic existence; it means no intrinsically existent production; it means the arising of effects whose nature is similar to a magician's illusion (in that it appears to be inherently existent, but it is not); ... it means emptiness and selflessness"

In Buddhism, an the effect is generally not ontologically independent of the cause. For example, in the teaching of Dependent Origination, each of the twelve conditions contains the first cause of ignorance within them, as described below:

There is the case where an uninstructed, run-of-the-mill person — who has no regard for noble ones, is not well-versed or disciplined in their Dhamma; who has no regard for men of integrity, is not well-versed or disciplined in their Dhamma — assumes form to be the self. That assumption is a fabrication. Now what is the cause, what is the origination, what is the birth, what is the coming-into-existence of that fabrication? To an uninstructed, run-of-the-mill person, touched by that which is felt born of contact with ignorance, craving arises. That fabrication [of self] is born of that. And that fabrication is inconstant, fabricated, dependently co-arisen.

SN 22.81

On seeing a form with the eye, he is infatuated with pleasing forms, and gets upset over unpleasing forms. He dwells with body-mindfulness unestablished, with limited awareness. He doesn't discern, as it has come to be, the awareness-release & discernment-release where those evil, unskillful qualities cease without remainder. Engaged thus in compliance & opposition, he relishes any feeling he feels — pleasure, pain, neither-pleasure-nor-pain — welcomes it & remains fastened to it. As he relishes that feeling, welcomes it, & remains fastened to it, delight arises. Now, any delight in feeling is clinging.

MN 38

It can be discerned in the quotes above, for example, feeling cannot arise without a form (sense object) and the feeling & delight must continue to persist for clinging (attachment) to arise & persist.

No effects can arise without multiple causes. The causes can still be in state just possible to arise or may vanished long time ago. The causes can be unreality as well, knowing person, car, etc. But it is impossible for every effect to arise without causes.

Although the aggregates, which called cancer, can arise without smoking, but that aggregates must cause by other various origins definitely. The doctor, practitioner, should find the other else instead.

That's why aggregates is called "sankhata (being caused by causes)".

in Madhyamika,the effect depends on the cause,wich one can say IS the effect because arising and Cessation do not occur.in Theravadan Kshanabhanga however,the effect is independant of the cause and the effect arises only when the cause has ceased.

a rather poor example, since cancers that are not caused by smoking are not the effect of smoking, so it has nothing to do with the question. and by definition, causality means the relation between cause and effect, so no, ontologically there can not be any effect without a cause.

and this is actually the precise approach for the noble truth on the eradication of suffering, since the eradication of the cause leads to the eradication of the effect. thus, eliminating craving, or tanha, one eliminates suffering or dukkha.