function resize(event){
    var lines = 0;
    var counter = 0;
    var delka = textarea.value.length;
    var sloupce = textarea.cols;
    var obsah = textarea.value;
        
    for (var i = 0; i < delka; i++) {
		counter++;
		
		if ((obsah.charCodeAt(i) == 10) || (counter > sloupce)){
			counter = 0;
			lines++;			
		}
    }
    
    if (lines < 3) lines = 3;                        
    
    textarea.rows = lines + 1;
}

function resize_back(event){
    textarea.rows = 4;
}

textarea.addEventListener("focus", resize, false);
textarea.addEventListener("keydown", resize, false);
textarea.addEventListener("blur", resize_back, false);

button.style.font = "bold 10pt Arial";

<textarea style="overflow: visible;"></textarea> je co?