First of all, excuse me if this question is too noobish.

I'm trying to understand how these things are relate: Curve type, its 'number of bits of security', size of the key and the maximum ciphertext size.

Comparing to RSA, I know, that size of the key directly affects the maximum size of ciphertext: it can never exceed the key size and in practice is even smaller than that.

Is this still holds for ECC?

If so, what's the limitations on the size of the key in terms of a specific Curve? Is it even possible to allocate keys of different sizes? Or, given that math is discrete, does each curve has a hard ceiling for a key size?

If on the other hand, the key size is unlimited, is it true that no matter how large it is, the effective hardness of encryption will never exceed the 'number of bits of security' of specific Curve? If so, does increase the key size only gives you a larger limit on the ciphertext size?