The absolute limitation on TCP packet size is 64K (65535 bytes), but in practicality this is far larger than the size of any packet you will see, because the lower layers (e.g. ethernet) have lower packet sizes.
The MTU (Maximum Transmission Unit) for Ethernet, for instance, is 1500 bytes. Some types of networks (like Token Ring) have larger MTUs, and some types have smaller MTUs, but the values are fixed for each physical technology.
This is an excellent question and I run in to this a lot at work actually. There are a lot of "technically correct" answers such as 65k and 1500. I've done a lot of work writing network interfaces and using 65k is silly, and 1500 can also get you in to big trouble. My work goes on a lot of different hardware / platforms / routers, and to be honest the place I start is 1400 bytes. If you NEED more than 1400 you can start to inch your way up, you can probably go to 1450 and sometimes to 1480'ish? If you need more than that then of course you need to split in to 2 packets, of which there are several obvious ways of doing..
The problem is that you're talking about creating a data packet and writing it out via TCP, but of course there's header data tacked on and so forth, so you have "baggage" that puts you to 1500 or beyond.. and also a lot of hardware has lower limits.
If you "push it" you can get some really weird things going on. Truncated data, obviously, or dropped data I've seen rarely. Corrupted data also rarely but certainly does happen.
At the application level, the application uses TCP as a stream oriented protocol. TCP in turn has segments and abstracts away the details of working with unreliable IP packets.
TCP deals with segments instead of packets. Each TCP segment has a sequence number which is contained inside a TCP header. The actual data sent in a TCP segment is variable.
There is a value for getsockopt that is supported on some OS that you can use called TCP_MAXSEG which retrieves the maximum TCP segment size (MSS). It is not supported on all OS though.
I'm not sure exactly what you're trying to do but if you want to reduce the buffer size that's used you could also look into: SO_SNDBUF and SO_RCVBUF.
According to http://en.wikipedia.org/wiki/Maximum_segment_size, the default largest size for a IPV4 packet on a network is 536 octets (bytes of size 8 bits). See RFC 879
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