From what I can gather, when encrypting with RSA key pairs, you cannot encrypt more data than the length of the key (at least I can't find the implementation in the libraries I'm using). So then, in order to encrypt larger amounts of data, you need to break it into chunks and encrypt the individual chunks. Please let me know if I'm incorrect about this assumption.
If the above assumption is true, I see this as similar to encrypting data with AES using ECB mode. This is obviously a bad idea as indicated by the following famous image:
Are there implementations of stream cipher or block-chaining like equivalents when using RSA key pair encryption which provides the expected level of pseudo-randomness over the entire data being encrypted?
Please feel free to comment on any assumptions I have made that may be incorrect.